Tuesday, 3 March 2015

Long Division with regrouping

I have taught Sonshine division using Montessori. From then, he is able to do mental division without regrouping i.e 266 divide 2 or 369 divide by 3.
Recently, I decided to teach Sonshine how to do long division that require regrouping and how to do the step by step working.
I tried teaching him by making him memorise the steps (which is a mix of division, multiplication and subtraction) but it didn't sit well with him. Realising that he needed to understand the technicalities behind the steps, I started to search for inspiration on how I can teach him. And lo and behold, I found it in our very own Primary 3 textbook. I was pleasantly surprised that our Math curriculum is adopting the Montessori method in explaining the subject to our kids. Finally someone up there see the good in Montessori Math! They have very wisely and cleverly combined the Montessori Math with the long division method. I was impressed!
Anyway, I studied it and presented to Sonshine exactly the way the textbook depicted. It worked!
 Here's how:
Let's work on this question 265 divide by 5.
You need Montessori 100, 10 and 1 stamps as well as green skittles. If you don't own these, you can easily make them using colored papers and simply writing the values on the paper. As for the skittles, you can use any objects really.

First, take out 2 hundreds, 6 tens and 5 ones to make 265.

265 is to be divided by 5, so take out 5 skittles. To make it more interesting. you can tell the child that there are 265 stamps to be distributed among 5 people. Pretend the skittles are people.
Next show the working as above.

Tell the child, always start with the largest value first. In this case, hundreds is the largest value. Next, he should try to distribute 2 hundreds to the 5 skittles. Notice, there is not enough hundreds to give out. The child has to convert all the hundreds into tens. 2 hundreds equals 20 tens.
Show the working:
Explain that the top part is the number of stamps distributed to each skittle. In this case, zero hundreds skittle was used. So put a '0' on top. And zero hundreds were distributed, hence '0' below the 2 under the hundreds column.  
After which, point out to the child after the conversion, he now has 26 tens (20+6) tens altogether. Show this in the working:
He can now distribute all the tens stamps.
Notice after distributing 25 tens stamps (5 tens stamps to each skittle) he has 1 ten stamps left over.
Divert the child's attention to the working. Tell the child that each skittle now has 5 tens stamps, hence have him write '5' on top of the working.
Ask him how many tens stamps did he distribute in total? There should be 25. Write it down in the working as shown above.
Remind him there were 26 tens stamps but he used only 25 stamps, hence there is 1 ten stamp left over as shown in the working.

Point out to the child that 1 ten is not enough to distribute to each of the skittle. Hence, he has to regroup or convert the ten into ones. He should now have 15 ones altogether.
Distribute all the one stamps to the skittles. Notice that there is no more stamps left. Show working:
Focus back to the working. Have the child count how many ones stamps did each skittle get. The answer should be '3'. Show in the working.
Also point out to the child that he had 15 ones stamps remaining and he has distributed all the 15 ones.

Have the child to count the number of stamps EACH skittle received. In this case, it is 53.
Point out to the child that there are no stamps left over. And the answer is 53.
Phew! I hope i didn't butcher the explanation. It is alot easier to explain in person then over the screen. If you intend to use this method to teach, you have to practise the steps out yourself first! Unless you are very certain, otherwise you will find yourself fumbling over throughout the lesson and you will lose your child's interest or worse, trust. If you didn't understand a single thing from the above, you can try studying the Singapore textbook, 'My Pals' for Primary 3 level.
Some things to note before embarking this lesson, the child must have a good grasp of the place values (2 hundreds is the same as 20 tens etc). He must be able to understand the meaning of division. It is important the child has a good foundation in his basics. Sonshine is able to grasp this because he was first taught the basics, read here. So he was able to understand the above concept very fast.
It may take a while for the child to 'see'. Practise makes perfect! Sonshine took this explanation very well and because of this method, he can now do long division regrouping mentally. All thanks to Montessori's very clear and visual explanation!

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